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Misc 20 - Chapter 7 Class 12 Integrals
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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Misc 20 Integrate the function (2 + sinβ‘2π₯)/(1 + cosβ‘2π₯ ) π^π₯ We can write integral as ((2 +γ sinγβ‘2π₯)/(1 + cosβ‘2π₯ )) π^π₯ = [(2 + sinβ‘2π₯)/(1 + (2 cos^2β‘γπ₯ β 1γ ) )] π^π₯ = [(2 + sinβ‘2π₯)/(2 cos^2β‘π₯ )] π^π₯ = [(2 + 2 cosβ‘γπ₯ sinβ‘π₯ γ)/(2 cos^2β‘π₯ )]ππ₯ = [2(1 +γ cosγβ‘γπ₯ sinβ‘π₯ γ )/(2 cos^2β‘π₯ )]ππ₯ = [(1 + cosβ‘γπ₯ sinβ‘π₯ γ)/cos^2β‘π₯ ]ππ₯ = [1/cos^2β‘π₯ +cosβ‘γπ₯ sinβ‘π₯ γ/cos^2β‘π₯ ] π^π₯ = [sec^2β‘γπ₯+cosβ‘γπ₯ sinβ‘π₯ γ/cosβ‘γπ₯ cosβ‘π₯ γ γ ] π^π₯ = [sec^2β‘γπ₯+tanβ‘π₯ γ ] π^π₯ = [tanβ‘γπ₯+sec^2β‘π₯ γ ] π^π₯ It is of the form β«1βγπ^π₯ [π(π₯)+π^β² (π₯)] γ ππ₯=π^π₯ π(π₯)+πΆ Where π(π₯)=tanβ‘π₯ π^β² (π₯)=sec^2β‘π₯ So, our equation becomes β«1βγ[(2 + sinβ‘2π₯)/(1 + cosβ‘2π₯ )] π^π₯ ππ₯=β«1βγπ^π₯ [tanβ‘γπ₯+sec^2β‘π₯ γ ]ππ₯γγ =π^π πππβ‘π+π
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo